RU2298768C1 - Method for measuring liquid volume discharge in pressure pipelines - Google Patents

Abstract

FIELD: measurement technology.

SUBSTANCE: method involves determining liquid discharge rate in axially symmetric flow cases by emitting ultrasonic impulses produced by acoustic converters through the pipeline cross-section center at given angle to flow movement direction and in the opposite direction, measuring impulses passage time in both directions, calculating average flow speed and measuring pipeline diameter in cross-section plane drawn through intersection point of the pipeline axis and impulses propagation ray. Two pairs of acoustic converters are used in axially asymmetric flow cases for determining liquid discharge, with ultrasonic impulses being emitted in mutually perpendicular planes.

EFFECT: high accuracy of measurements.

2 cl, 11 dwg

Description

The invention relates to methods for measuring fluid flow in pressure pipelines with axisymmetric and non-axisymmetric flows.

There is a method of determining the volumetric flow rate of a fluid in a hydraulic installation, which consists in measuring the parameters of a fluid flow by forming an acoustic beam between two acoustic transducers and determining a volumetric flow rate of a fluid based on the measured parameters (RF patent No. 2201579, class G 01 F 1/66, 2003 [one]).

A disadvantage of the known method [1] is its limited use, in particular, this method can be implemented in hydraulic installations with spiral chambers and stator columns placed in them.

Known from the patent of the Russian Federation No. 2112928, class. G 01 F 1/66, 1998 [2] a method for measuring the flow rate of flowing liquids, comprising determining the average velocity, calculating the flow rate using ultrasonic pulses radiated at an angle to and against the direction of flow.

Known from the patent of the Russian Federation No. 2069314, class. G 01 F 1/66, 1996 [3], which includes emitting an ultrasonic signal at an angle to and against the direction of fluid flow, measuring the transit time of the ultrasonic signal, calculating the average velocity of the fluid flow, and calculating the fluid flow.

A common drawback of the methods known from [2] and [3] is the insufficiently high measurement accuracy and low versatility due to the inability to use in pressure pipelines.

The technical result that is achieved by using the invention is to increase the accuracy of measuring the flow rate of the fluid and expand technological capabilities by providing measurements of the parameters of the flow of fluid flowing in pressure pipelines of complex configuration, with a variable cross-section and with axisymmetric and non-axisymmetric flows.

The achievement of the specified technical result is ensured by the fact that in the claimed method of measuring fluid flow in pressure pipelines with a variable cross-section and with an axisymmetric flow, an acoustic transducer, an ultrasonic pulse is emitted through the center of the cross-section of the pipeline at an angle to the direction of flow of the fluid and against the direction of flow, measure time the passage of the ultrasonic pulse in both directions, calculate the average velocity of the flow in the pipeline, measure the diameter t uboprovoda in its cross-sectional plane passing through the point of intersection of the axis of flow and the ultrasonic pulses propagation path, and determine the liquid flow.

In another embodiment of the method, when measuring fluid flow with non-axisymmetric fluid flows, two pairs of acoustic transducers are used, each of which emits and receives an ultrasonic pulse directed through the center of the cross section of the pipeline at an angle to the direction of movement of the fluid flow and in the opposite direction, and measure the propagation time of ultrasonic pulses, while pairs of acoustic transducers are placed on longitudinal mutually perpendicular planes passing through the axis of the pipes wires, wherein the intersection of the ray propagation of the ultrasonic pulses provided either at one point on the pipe axis, or in two diversity technique along axis calculating the average flow velocity in each plane, and determining the flow rate as an average costs in arrangement planes of each pair of acoustic transducers

Figure 1 presents the plot of speeds in an axisymmetric flow.

Figure 2 shows a schematic diagram for determining the average flow rate by the diameter of the cross section of the pipeline.

Figure 3 shows a conical section of the pipeline.

Figure 4 shows the dependence of the total loss coefficients in the diffuser channel on the Reynolds number.

Figures 5, 6 and 7 show the velocity fields formed after the knees.

On Fig shows a method for determining velocity plots for non-axisymmetric cross-section.

Figure 9 shows a schematic diagram of determining the flow rate for non-axisymmetric flows in pressure pipelines.

Figure 10 shows the layout of two pairs of acoustic transducers when determining the flow rate for non-axisymmetric flows.

Figure 11 shows a diagram of the arrays of placement of acoustic transducers in a diffuser on an existing installation.

Axisymmetric flows in pipes are formed in rectilinear extended sections with lengths of at least 15 diameters up to the flow measuring target and 5 diameters after it.

Experimental studies performed for these conditions showed that the velocity profile along the diameter of the pipeline when counting along the X axis from the center to the wall obeys a power law in the form:

where v is the magnitude of the speed at a distance X from the center of the cross section of the pipeline (see figure 1),

U ₀ - maximum speed in the center of the cross section of the pipeline,

x is the distance from the center,

R ₀ is the radius of the cross section of the pipeline.

The volume of the body of revolution (Fig. 1), expressing the flow rate Q, is determined by the double integral in the form:

This expression after conversion takes the form:

where m is an exponent depending on the Reynolds number (table 1).

Table 1 Re 4 × 10 ³ 10 ⁵ 10 ⁶ > 10 ⁶ m 1/6 1/7 1/9 1/10

The average speed for any diameter of the cross section of the pipeline is:

This property for conditions of axisymmetric flow is widely used in systems of ultrasonic measurements of volumetric flow rates of liquids.

Figure 2 shows a schematic diagram of determining the average speed by the diameter of the cross section of the pipeline, in accordance with which the acoustic transducers are installed at points a (AP1) and b (AP2) and operate alternately in the receiver-emitter mode.

The propagation times of the ultrasonic pulse from point b to point a (t ₁ ) and from point a to point b (t ₂ ) can be represented as:

where L _a is the length of the active part of the acoustic beam, m (from point "a" to point "b);

With ₀ - the speed of ultrasound in still water, m / s;

t ₁ and t ₂ - the propagation time of the ultrasonic pulse along the stream and against it, s;

V _np is the average velocity of the projections of axial velocities onto the acoustic beam, determined by the formula:

from equations (4) and (5), given that

The technical means of ultrasonic flow meters measure t ₁ and t ₂ .

The average speed along the diameter of the cross section of the water conduit is determined by the calculation according to the formula: V _cp = V _np / cos (α) or after conversion from the expression:

The calculation of the flow rate is performed as

where K _k is the correction coefficient, the value of which is 0.92-1.1

(the value of the correction coefficient from one or higher can be obtained if the acoustic luz is traced not along the axis of the pipeline, but along the chord, since theoretically, at a constant speed over the entire cross section of the pipeline, the correction coefficient is unity);

F is the cross-sectional area of the pipeline (F = πR ² ).

The proposed method for measuring volumetric flow in conical transitions of pipelines is based on the following research results.

Free turbulence can develop by a jet formed by a fluid flowing from a round pipe into a large volume of the same fluid.

It has been established that the angle of expansion of the stream does not depend on the type of liquid in the stream and the surrounding space if there are no compressibility and cavitation effects. It follows that the averaged motion and large scales of turbulence are independent of the density, viscosity, and Reynolds number, provided that the latter is large enough to ensure completely turbulent motion. The velocity profiles of different sections of such a jet, although varying in width and height, have a similar shape and can be reduced in dimensionless coordinates to a single curve.

These conclusions are also valid for the case of fluid flow in a conical transition, if the cone’s opening angle does not exceed the free-stream opening angle at the Reynolds number, which ensures the full development of the turbulent flow.

Figure 3 shows a conical section of the pipeline with an opening angle α.

The calculated diameter D ₀ , the value of which is introduced in the formula (8) for determining the flow rate, is determined in the cross section passing through the point 0 of the intersection of the acoustic beam with the axis of the cone. Sections with diameters D ₁ and D ₂ are placed at distances L ₁ and L ₂ :

and the size of the diameters is determined by the expressions:

The lengths of sections l _0-1 and l _{0-2 of the} acoustic beam will be different, namely: l _0-2 > l _0-1 - for flows both in the diffuser and in the confuser.

However, the average speeds will be equal. This follows from the above expressions:

- the average speed on the plot l _0-1 :

After the expansion of the integral, v _0-1 = V ₀ / m + 1

- the average speed in the area l _0-2

After the expansion of the integral, v _0-2 = V ₀ / m + 1.

In formulas (11) and (12), counting x over lengths l was carried out in the direction from the pipeline wall to the center (to point 0).

Acoustic ray tracing angle β is usually recommended to be equal to 45 °, but it can also be changed in accordance with the specific conditions of the pipeline construction.

The cone opening angle α is taken no more than 5-7 ° both for conical sections of the pipeline and for various nozzles.

Figure 4 shows the dependence of the total loss coefficients in the diffuser channel on the Reynolds number. At Re≈3 × 10 ³ and higher, the process of turbulization of the flow captures the region of the uninterrupted boundary layer, which increases its resistance to separation (at α = 7 °, separation is eliminated).

At α = 15 ° and Re = 10 ⁵ ÷ 2 × 10 ⁵ , the turbulent boundary layer breaks off and the losses increase. The range of diffuser opening angles of 10 ° <α <15 ° defines a group of diffusers with an unstable flow pattern.

The active influence of the Re number practically ceases at Re = 2 × 10 ⁵ . For Reynolds numbers Re> 2 × 10 ⁵ , a self-similarity region is established.

When designing hydraulic systems, which include conical sections, opening angles from α = 5 ° to α = 7 ° are usually assigned, which ensures continuous flows.

Thus, for large Reynolds numbers and an axisymmetric flow in conical transitions, accurate flow measurement is ensured by directing the ultrasonic pulse at an angle to the direction of the fluid flow and back with the intersection of the conduit axis, measuring the transit time of the ultrasonic pulse, calculating the average flow rate in the pipeline, and measuring the diameter of the pipeline in the plane of its cross section passing through the point of intersection of the axis of the conduit and the beam of the ultrasonic pulse, and the flow rate is determined by to

Q = K _k V _{0 cf.} πD ^2/4, wherein D ₀ ≠ (D ₁ + D ₂₎ / 2.

He axisymmetric flows are formed after local hydraulic resistances such as gate valve, ball valve, elbow, tees and their combinations.

Figure 5, 6 and 7 shows the velocity field formed after the knees. Figure 5, in particular, shows the velocity field in the pressure pipe of the Vazuz hydro-technical system. The section is removed at a distance of 6.6 D of the pipeline from the axis of the pump and elbow. The region of maximum speeds is offset from the axis of the pipeline by about half the radius.

Figure 6 shows the velocity field behind the elbow of the suction pipe before entering the impeller of the pump OP-11-135. In this case, the region of maximum velocities is also shifted by about half the radius.

Figure 7 shows the velocity field after the knee at the entrance to the siphon outlet. Here, the region of maximum velocities is also shifted by the same half of the radius.

Table 2 shows the average values of the velocities in sections, indicated in increments of the angle through 22.5 ° (Fig.7). If you determine the average value of the speed in only one section, then the error can reach 0.76%. When using the definition of the average velocity for two mutually perpendicular diameters, the error decreases by 3.5 times or more (see table 3).

On Fig shows a method for the theoretical determination of velocity plots in a non-axisymmetric flow. The location of the point with the maximum velocity V ₀ on the radius is determined by the expression (1-n) R ₀ , where n can vary from zero to one. The minus sign in the expression R _B (see Fig. 8) is taken at an angle A from zero to 90 °, and the plus sign at an angle A, starting from A = 90 ° to 180 °. The average speed at a radius of R ₀ is equal to

The average speed at a diameter of 2R ₀ can be determined by the expression:

The integrand in expression (15) cannot be reduced to elementary functions, i.e. this integral refers to the elliptic form solved by numerical methods.

Table 5 shows the results of such calculations for R ₀ = 1, v ₀ = 1, n = 0.5, m = 0.1 (Re> 10 ⁶ ). Theoretical calculations quite well confirm the experimental data (table 3),

table 2 The average values of the velocities in sections (Fig.7 - experimental data) Section number Angle α ° Speed V _cp Deviation% one 0 0.8542 +0.32 2 22.5 0.8532 +0.20 3 45.0 0.8517 -0.02 four 67.5 0.8500 -0.18 5 90.0 0.8450 -0.76 6 112.5 0.8492 -0.27 7 135.0 0.8532 +0.20 8 157.5 0.8558 + 0.50

ΣV _cp /8=0.8515

Table 3 Average values of speed along two mutually perpendicular planes (according to the results of table 3) Section No. V _cp Deviation 1 and 5 0.8496 -0.22 2 and 6 0.8512 -0.04 3 and 7 0.8524 +0.11 4 and 8 0.8529 +0.16

ΣV _cp /4=0.8515

Table 4 Average values of velocities over sections (calculation) Section number Angle α ° Speed V _cp Deviation% one 0 0.9134 +0.47 2 22.5 0.9126 +0.38 3 45.0 0.9091 0.00 four 67.5 0.9081 -0.11 5 90.0 0.9048 -0.47 6 112.5 0.9056 -0.38 7 135.0 0.9091 0.00 8 157.5 0.9101 +0.11

ΣV _cp /8=0.9091

Table 5 Average values of speed along two mutually perpendicular planes (according to the results of table 4) Section No. V _cp Deviation% 1 and 5 0.9091 0 2 and 6 0.9091 0 3 and 7 0.9091 0 4 and 8 0.9091 0

ΣV _cp /4=0.9091

Table 5 shows the average values of speed over two mutually perpendicular sections. In this case, the error in determining the average velocity is zero, if you do not take into account the error of the technical means of measurement.

The considered results of experimental studies and calculations allow us to establish that:

- an accurate determination of the flow rate of non-axisymmetric flows can be ensured by measuring average velocity values along mutually perpendicular planes;

- while mutually perpendicular planes can be placed in a cross section arbitrarily;

- the error in determining the flow rate depends only on the errors of the applied technical means, while the fluid flow rate is determined as the average value of the flow rate in the indicated planes.

A practical solution to the developed method for determining the volumetric flow rate of a liquid can be implemented by using ultrasonic flow meters.

Figure 10 shows the placement of two pairs of acoustic transducers in mutually perpendicular planes.

There are two possible applications of technical means of measurement.

One of them allows the intersection of two acoustic rays on the axis of the conduit at one point (point O, figa). In this case, in order to avoid the mutual influence of acoustic rays, technical means must ensure synchronization of the alternating operation of each pair of acoustic transducers

In another case, the intersection points of the acoustic rays with the axis of the conduit are spaced apart by ΔL (Fig. 106), which allows the use of two independent sets of technical means.

Figure 11 shows a diagram of the arrays of placement of acoustic transducers in a diffuser on an existing installation. The opening angle of the diffuser is 6.14 °. The intersection points of the acoustic rays with the axis of the diffuser are spaced ΔL = 150 mm. The breakdown of the placement of acoustic transducers made according to equations (9) and (10). The beam of the acoustic transducers AP3 and AP4 in figure 10 is rotated 90 ° and is shown conditionally in the plane of the beam AP1-AP2.

Flow measurements were made by flow meters of the UFM-005 type, i.e. two independent systems. The measurement results were transmitted to the SIK-4 type adder. On the adder, the automatic summation of the two measurement results was performed, and the sum was divided in half. This flow measurement system was put into trial operation in October 2004.

Table 6 compares the results of the experiments with the calculations (the ratio of the maximum average to minimum)

Table 6 Name The average value of the cross-sectional velocity with V _max (calculation and model in relative units, nature in m ³ / h) The average value of speed along mutually perpendicular sections Value Ratio (2) / (3) Deviations in% Payment 0.9134 0.9048 1,0095 -0.04 Model Experience 0.8542 0.8450 1,0109 +0.10 Experience on an existing installation 7630 7560 1,0093 -0.06

For these parameters, there is also a close coincidence of the experimental data with the calculations, which leads to high measurement accuracy when implementing the method in practice.

Claims (2)

1. The method of measuring the volumetric flow rates of fluid in the conical transitions of pressure pipelines with an axisymmetric flow, which consists in emitting an acoustic transducer through the center of the cross section of the pipeline of the ultrasonic pulse at an angle to the direction of flow and in the opposite direction, measuring the transit time of the ultrasonic pulse in both directions, calculating the average the flow rate V _cp in the pipeline, measuring the diameter of the pipeline D ₀ in the plane of the cross section passing through point p intersection of the axis of the pipeline and the beam of propagation of ultrasonic pulses, and the determination of fluid flow by the formula Q = K _k V _{0 cf.} πD ^2/4, where K _k is the correction factor. 2. A method for measuring the volumetric flow rates of liquid in pressure pipelines with an axisymmetric flow, which consists in using two pairs of acoustic transducers, each of which emits and receives an ultrasonic pulse directed through the center of the cross section of the pipeline at an angle to the direction of movement of the fluid flow and in the opposite direction, measuring the propagation time of ultrasonic pulses from each pair of acoustic transducers, while the pairs of acoustic transducers are located on mutually perpendicular planes passing through the axis of the pipeline, and the intersection of the propagation rays of ultrasonic pulses is provided either at one point lying on the axis of the pipeline, or at two points spaced along the axis, measuring the average flow velocity in each plane and determining the flow rate as the average value costs in the planes of the location of each pair of acoustic transducers.

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